A073340 Fibonacci prime pairs: the indices of each pair differ by two and the relevant Fibonacci numbers are both prime.

3, 5, 5, 7, 11, 13, 431, 433, 569, 571

Offset

1,1

Comments

There are no other Fibonacci prime pairs up to Fibonacci(104911). (See A001605.) Are there any larger terms?

References

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, Rev. ed. 1997, p. 46.

Links

Table of n, a(n) for n=1..10.

Example

The 431st Fibonacci number and the 433rd Fibonacci number are both prime and their indices differ by 2.

Mathematica

Flatten[Select[Partition[Select[Range[3000], PrimeQ[Fibonacci[ # ]]&], 2, 1], #[[2]] - #[[1]] == 2 &]]

Prog

(Python)
from sympy import isprime
def afind(limit):
  i, fnm2, fnm1 = 1, 1, 1
  while i < limit:
    if isprime(fnm2) and isprime(fnm2 + fnm1):
      print(i, i+2, sep=", ", end=", ")
    i, fnm2, fnm1 = i+1, fnm1, fnm2 + fnm1
afind(600) # Michael S. Branicky, Mar 05 2021

Crossrefs

Cf. A000045, A001605, A279795, A281087.

Sequence in context: A069201 A272882 A077800 * A118409 A162779 A158284

Adjacent sequences: A073337 A073338 A073339 * A073341 A073342 A073343

Keyword

more,nonn

Author

Harvey P. Dale, Aug 25 2002

Extensions

Offset changed to 1 by Joerg Arndt, Jan 18 2017

a(1) and a(2) prepended by Bobby Jacobs, Jan 18 2017

Status

approved